Comparizer Ideals of Rings#.

A right ideal I of a ring R is called a comparizer right ideal if for all right ideals A, B of R, either A ⊆ B or BI ⊆ A. For every ring R there exists the largest comparizer ideal C1(R) of R, and higher comparizer ideals Cα(R) can be defined inductively. In this paper, comparizer right ideals and relationships between the iterated comparizer ideal and some classical radicals of R are studied. Obtained results generalize some properties of right chain rings, right distributive rings, right Bezout rings and rings with comparability. [ABSTRACT FROM AUTHOR]